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15. A MATHEMATICAL MODEL FOR MALARIA WITH OPTIMAL CONTROL AND COST-EFFECTIVENESS ANALYSIS by Adamu A.K. Atureta M.S. Adamu M.M and Kwami A.M Volume 52 (July & Sept., 2019 Issue)
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A MATHEMATICAL MODEL FOR MALARIA WITH OPTIMAL CONTROL AND COST-EFFECTIVENESS ANALYSIS

Adamu A.K.  Atureta M.S.  Adamu M.M  and  Kwami A.M

Department of Mathematics & Statistics, Federal University Wukari, Taraba State, Nigeria

Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi State, Nigeria

Abstract

Many infectious diseases including malaria are preventable, yet they remain endemic in many communities due to lack of proper, adequate and timely control policies. In this paper, we formulated an human-mosquito malaria model by introducing a new compartment for immuned human population, a partially immune compartment to account for waning immunity and also incorporate a vector reduction parameter in the vector population. The impact of vaccination and vector reduction were further investigated by incorporating time dependent controls using Pontryagin’s Maximum Principle (PMP). We apply the optimal control strategy to investigate and analyze the optimal cost for controlling the transmission of malaria using vaccination, treatment and indoor residual spray as control parameters. Some numerical simulations were carried out to confirm the analytic results and possible behavior of the model. The result of the optimal control and cost effectiveness analysis shows clearly that malaria can best be controlled with the combination of vaccination and indoor residual spraying (vector reduction).  

Keywords: Incremental cost effective ratio, Pontryagin’s Maximum Principle, Optimal cost, Indoor residual spray.

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